There's a word for this isn't there? Can anyone help me out.

Also, is there a term for a piece of music with a peculiar combination key signature eg Bb and F sharp?

Thanks clever peeps.

Bitonality (or polytonality). I think Stravinksy uses it sometimes. Also Milhaud?

Not sure about the odd key signature thing.

I agree that Bi-tonality is correct. The odd key signature would simply be called a non-standard key signature. Are you playing Bartok perhaps?

I don't think it has to be hyphenated. 'Bi' is just a normal prefix, like 'un' or 're'. Although I could be wrong...

My mistake I think.

Don't worry; show me that lissom inside leg you mention and I'll forgive you.

I agree, it would be bitonality, or polytonality if theres more than two, although I don't know who has done this.

I didn't know there was a word for certain combinations of keys though.

If in doubt, check with the AB Guide to Music Theory (Part 2)! Pages 244 and 245 refer to polytonality (of which bitonality is one version). An example is quoted from Bartok where 2 bracketed staves are shown, the upper with a Treble Clef and the key signature for E major and the lower with a Treble Clef and the key signature for A flat major.

Presumably it's not essential to have two different key signatures, if accidentals were used to the same effect? Or is that missing the point?

Absolutely correct - it's just that the Bartok example quoted above makes it crystal clear that 2 keys are being used at the same time in the piece.

we learned it as polytonality

The Holst "Terzetto" is in three different keys. See here

Yes that's correct, but 'poly' (many) is simply an extension of 'bi' (two); they're not two different concepts.